We show that sensorial delay alters the collective motion of self-propelling agents with aligning interactions: In a two-dimensional Vicsek model, short delays enhance the emergence of clusters and swarms, while long or negative delays prevent their formation. In order to quantify this phenomenon, we introduce a global clustering parameter based on the Voronoi tessellation, which permits us to efficiently measure the formation of clusters. Thanks to its simplicity, sensorial delay might already play a role in the organization of living organisms and can provide a powerful tool to engineer and dynamically tune the behavior of large ensembles of autonomous robots.

Rafal Piwowarczyk defended his Master thesis in Complex Adaptive Systems at Chalmers University of Technology on 19 February 2018

​Title: Influence of Delay on the Vicsek Model

The aim of this work is to show that sensorial delay influences the behaviour of self-propelling agents using self-aligning interactions. The model was based on the Vicsek model, which is a two-dimensional system of self-propelling particles that are able to detect and align with each other within a certain radius. We prove that the introduction of short delays favours cluster and swarm formation, while extending the delay to higher values or implementation of negative delays significantly harms this process. We introduce a global clustering parameter, which is based on the use of the Voronoi tessellation, which allows us to measure the emergence of clusters. The sensorial delay might play a crucial role in systems that exhibit swarming behaviours and it’s better understanding can result in the construction of key tools for the realisation and manipulation of complex networks of autonomous robots.